A Boston private equity firm will invest $134.7 million in struggling Sterling Financial Corp. as part of the Spokane company’s ongoing efforts to raise enough money to meet requirements imposed by federal regulators.

As part of that recapitalization effort, Sterling also said it entered into an exchange deal with the U.S. Treasury that will convert about $303 million in preferred shares held by Treasury to common stock worth about $75 million, the company said in a news release.

The two deals were described as linked, with the Treasury deal depending on Sterling signing the deal that will raise the $134.7 million from Thomas H. Lee Partners, L.P.

Company executives have said in the past that it’s rare for Treasury to accept such a steep discount on its investments, made as part of the Troubled Asset Relief Program.

Hoovers, an industry information clearinghouse, describes Thomas H. Lee as a “friendly leveraged buy-out company” that prefers to work with distressed companies to improve shareholder value.

Normally, Sterling shareholders would have to vote on the equity investment. But Sterling obtained an exemption that allows the deal to take place because any delay could “seriously jeopardize” the bank’s viability, the news release noted.

The investment from Thomas H. Lee L.P. and the Treasury exchange are part of efforts by Sterling to raise a total of about $720 million needed to meet “all of its federal capital requirements,” the company said in its release.

Also today, Sterling reported a first-quarter loss of $88.8 million, or $1.71 per common share. That compares with a first quarter 2009 loss of $24.8 million, or 48 cents per share.

Read more background on Sterling Financial Corp. and its subsidiary, Sterling Savings Bank.